21 citations · 43 across the 29 of their papers we have counts for
4 papers · 1 filter
A new type of deterministic Salem sets and its spectrality
Chun-Kit Lai, Ruxi Shi, Yu-Hao Xie
For all , we provide a new deterministic construction of Cantor sets whose Fourier dimension and Hausdorff dimension are both equal to . The construction is based on…
Dynamical dimension and shift embeddability without the marker property
Ruxi Shi
We study the aperiodic inverse-limit system constructed in our earlier work as an example of a finite-mean-dimensional dynamical system without the marker property. We prove that i…
Fuglede's conjecture holds for three intervals
Ruxi Shi
We prove that every bounded measurable subset of the real line that is both spectral and a union of three intervals tiles the line by translations, thereby completing Fuglede's con…
A variational principle for metric mean dimension via lower Brin-Katok local entropy
Ruxi Shi
We prove a finite-scale comparison between lower Brin-Katok local entropy and Katok covering entropy. Let be a compact metric topological dynamical system and l…